1. Field of the Invention
This invention pertains to a measurement circuit for a half bridge resistance strain gage and, more particularly, to a bridge circuit in which the cable resistance is placed in series with very high resistance completion resistors to eliminate the apparent strain errors due to changes in cable resistance produced by heating.
2. Prior Art
FIG. 1 illustrates a prior art strain gage as used in a conventional Wheatstone bridge circuit, comprising an active resistor (RA) 101, a dummy resistor (RD) 102, a first completion resistor (RCA) 107, and a second completion resistor (RCB) 108.
In a typical application, the active and dummy resistors are attached to a member which is subject to strain; however, the strain is transmitted only to RA. This member is often located in a higher temperature area, making it necessary to remotely locate the remainder of the circuitry. For example, the completion resistors are typically located remotely from the active and dummy resistors by means of leads which are represented in FIG. 1 by their equivalent resistances (RLA) 103A, (RLB) 103B and (RLC) 103C. FIG. 1 also shows a temperature compensating resistor (RTC) 105 and a balancing resistor (RBAL) 106 placed in series between lead 103A and RCA to aid in temperature compensating the bridge. Power for the bridge is supplied from a source 110 and is applied to the bridge at the junction of the balancing resistor and the temperature compensating resistor, and at the junction of the lead 103B and the completion resistor RCB. The bridge output voltage is measured at terminals 109 which are located in series with lead 103C and the junction of the completion resistors RCA and RCB. It should be noted that although leads 103A, 103B and 103C are drawn as separate lines, they may be joined in a single cable or run as shown, depending on the application.
In a fundamental Wheatstone bridge circuit, there are only four resistors, RA, RD, RCA and RCB. The circuit of FIG. 1 can be viewed as such a circuit by considering the value of all other resistors as zero. In the operation of this circuit, the bridge is initially adjusted to provide an output voltage at terminals 109 of zero volts. This is referred to as zero setting or zeroing. To zero set the bridge, the voltage produced at the junction of the RA and RD must be equal to the voltage produced at the junction of RCA and RCB. Since RA and RD form a first voltage divider supplied by source 110, and RCA and RCB from a second voltage divider supplied by the same source, the following relationship may be written: EQU RA/(RA+RD)=RCA/(RCA+RCB) and, (1) EQU RD/(RA+RB)=RCB/(RCA+RCB) (2)
By dividing these two equations the following equation results: EQU RA/RD=RCA/RCB (3)
Equation (3) is a well known equation showing the relationship of the resistance in each arm of the Wheatstone bridge.
In the most common applications of the Wheatstone bridge, the value of an unknown resistance is found by inserting it in the bridge circuit to form one arm of the bridge. The value of one or more of the other known resistances in the bridge arms are then varied to produce a zero output voltage. The resulting values of the known resistors after adjustment are substituted in Equation (3) to find the value of the unknown resistor.
In strain gage applications, the bridge is used in a different manner, but the equations still applied. In strain gage applications, the resistances are all known values, but the active element is placed under strain (elongated or compressed) by bonding or welding it to a structural member under test which is subject to a strain. The resistance of the active element, RA, changes in a known manner as it is strained, making a measurement of its resistance an indicator of the strain being experienced by the member under test. The measurement of the change in resistance of the active element is made by measuring the change in the output voltage. Unlike the conventional use of the bridge, no attempt is made to zero the bridge after the initial zeroing. The value of the remaining resistors in the bridge are left unchanged.
The output voltage is given by the difference between the two voltage divider outputs: ##EQU1##
The change in output voltage with respect to the change in the active resistance is found by differentialing equation (4): ##EQU2## A gage factor, F, is defined as follows: ##EQU3## Where: dR.sub.A =The change in the resistance RA
R.sub.A =The value of resistance of the active resistor PA0 dL=The change in the length of the member strained PA0 L=The length of the member over which the strain is measured.
The strain gage factor may be considered as the ratio of the percent change in the resistance of R.sub.A to the percent change in length of the member under test.
Substituting the gage factor F into Equation (5), we have: ##EQU4## Where RA and RD are equal, Equation (7) reduces to: ##EQU5## If the bridge is zeroed first, Equation (8) represents the output voltage E.sub.out as indicated in Equation (9) ##EQU6##
Where the active resistor is subject to a temperature that differs from that of the dummy resistor, or these resistors have a different temperature coefficient, the circuit may be compensated by using a temperature compensating resistor RTC 105. However, the addition of the RTC upsets the zero balance of the bridge. To overcome this and balance the bridge, the balancing resistor RBAL 106 is added. In a practical circuit, the RTC and RBAL are small in comparison to the other resistors in the bridge. For example, the active, dummy and completion resistors are typically in the order of 120 ohms, while the temperature compensating and balancing resistors are typically 15 ohms.
Although the prior art circuitry is commonly used, it presents a number of serious problems in obtaining accurate results. The principal problem occurs when both the gage elements and the cable are subjected to varying temperatures which change their resistances by very sizeable amounts. Despite the fact that the cable resistances 103A, 103B and 103C in each leg approximately track each other, the effects of heating in the two arms of the bridge to which 103A and 103C are connected are not simply accounted for. The reason for this can be understood by noting that the contribution of each bridge arm to the output signal is proportional to its change in resistance divided by its total original resistance or .DELTA.R/R. Even though .DELTA.R may be the same in both arms of the bridge, R never is the same so that .DELTA.R/R is different for the two arms, resulting in a zero shift or apparent strain signal from merely heating more or less cable than was heated during temperature calibration.
Unfortunately, the temperature compensating resistor RTC 105 exaggerates this effect and the magnitude of the error is impossible to theoretically predict to an acceptable accuracy, making it necessary to characterize the gage and cable by measurement with different amounts of cable held at elevated temperatures. Such measurements provide an apparent strain which depends on gage temperature and actual cable resistance. The variable cable resistance also changes the strain sensitivity of the active arm of the bridge, making knowledge of the cable resistance important for accurate results. It is not convenient to measure these resistance because the gage portion of the bridge must be disconnected from the remainder of the bridge.
The measurement of the cable resistances can be simplified by adding additional leads, referred to as cable conductors, which permit the cable resistance to be measured directly without disconnecting the cable leads, but data correction is complicated and true compensation is usually not obtained, except in very controlled circumstances of cably heating, not often achieved in practical cases.